Question

Using the defects method, which of these relationships represents the Law of Cosines if the measure of the included angle between the sides a and b of ∆ABC is more than 90°?

a.area of square c2 = -area of square a2 – area of square b2 + area of defect1 + area of defect2
b. area of square c2 = area of square a2 + area of square b2 + area of defect1 – area of defect2
c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2
d. area of square c2 = area of square a2 + area of square b2 + area of defect1+ area of defect2
e. area of square c2 = area of square a2 - area of square b2 + area of defect1 - area of defect2

Answer 1

"area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2" is the one relationship that represents the Law of Cosines if the measure of the included angle between the sides a and b of ∆ABC is more than 90°. The correct option among all the options that are given in the question is option "c".

Answer 2

Answer: c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2

(Option C)

Explanation:

The cosine rule helps to determine the different angles and sides of a triangle. The cosine rule is helpful when you need to find the third side of the triangle when the other two sides of the triangle are given  and the angle between them.